Adaptive Control for Reducing Nonlinear Vibrations of a Flexible Arm

Abstract

Robotic arms have a great range of applications in high precision industries, however the flexibility of the robotic arm affects the precision substantially. In this paper, a new nonlinear model for a flexible arm is presented. The arm consists of a series of distributed lumped masses that are able to vibrate vertically and rotationally. The equations of motion are derived for a fixed position on which the external forces and moments are imposed. An adaptive control algorithm for a series of virtual absorbers is developed to suppress the oscillations of the lumped masses which have nonlinear stiffness. Regardless of the main system uncertainties, the results indicate successful performance that the virtual absorbers can simultaneously attenuate the system oscillations.